Episode 54 - Umaswati - Mind the Gap

In this episode of The Mathematicians Podcast, I am jumping ahead 800 years and travelling 5,000 km back to India to pick up the threads of a fascinating mathematical tradition. I’ll be introducing you to Umaswati, a pivotal figure from around the 2nd Century CE who helped systematise the teachings of Jainism, a religion where "Right Knowledge" and the study of the cosmos made maths a fundamental pursuit.

Together, we explore the four broad periods of Indian religious development: Vedic, Śhramana, Puranic, and Bhakti, and see how the Jain tradition carved out a unique space for mathematical inquiry. We’ll discuss:

• The approximation of \pi : Why the Jains used \sqrt{10} and how they handled circular segments.

• The power of place value: How ancient Indian poets and scholars were comfortably using numbers as large as 10^64 while the Greeks were still stuck at the Myriad

• The Five Types of Infinity: Long before Georg Cantor revolutionised set theory in the 19th century, Umaswati and the Jain scholars were already classifying different scales of the infinite and the transfinite.

Join me as I navigate the intersection of faith, philosophy, and the infinite.

You can find Ben on Bluesky @mathematicians-pod. You can support him at ko-fi.com/benjamincornish.

Hashtags:#Maths #HistoryOfMaths #Mathematics #Jainism #Umaswati #India #History #Infinity #LargeNumbers #AncientIndia #STEMPodcast #TheMathematiciansPodcast

Keywords:Umaswati, Jaina Mathematics, Indian Mathematics, History of Maths, Brahmanism, Vedic Tradition, Śramaṇa, Mahabharata, Place Value System, Transfinite Numbers, Enumerable and Innumerable, Pi Approximation, Mathematical Philosophy, Ancient Indian Scholars.

The music was- "Danse Macabre - Finale" Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 http://creativecommons.org/licenses/by/3.0/